Asymptotic confidence intervals after using Akaike's information criterion for variable selection.

The mere fact of selecting variables introduces randomness. One should not ignore this model selection step in inference after selection by pretending the selected variables to have been specified beforehand. We study the asymptotic distribution of parameter estimators after model selection with Akaike's information criterion.

We exploit the overselection property of this criterion in the construction of a selection region, and obtain the asymptotic distribution of parameter estimators and linear combinations thereof in the selected model. The proposed method does not require the true model to be in the model set. We developed a simulation approach to use the resulting distributions-post-selection and to calculate confidence regions for the model parameters.

This is joint work with A. Charkhi.

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